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Title: | Cubic equations over p-adic field and their applications | Authors: | Mohd Ali Khameini bin Ahmad | Subject: | Equations, Cubic p-adic numbers p-adic field |
Year: | 2016 | Publisher: | Kuantan :International Islamic University Malaysia, 2016 | Abstract in English: | In this thesis, we did a research on cubic equations over p-adic field Qp where p is a prime number. In the first part, we studied the general cubic equations over Qp where p >3. We described the location of roots of the general cubic equation without knowing their exact values. Furthermore, we gave the solvability criterion and the number of roots of the general cubic equation over Zp; Zp \ Zp; Qp nZp and Qp. In the second part, we discussed the depressed cubic equations over p-adic field. We provided the exact location of roots of the depressed cubic equation over p-adic field for p > 3. For p = 3, we provided the solvability criterion and the number of roots of the depressed cubic equation over Z3; Z3 \ Z3; Q3 \ Z3 and Q3. While, for p D 2, we provided the solvability criterion of the depressed cubic equation over Z2; Z2 \ Z2; Q2 \ Z2 and Q2. In the last part, we presented the application of the cubic equations in the p-adic Potts model. We described all translation invariant p-adic Gibbs measures for the Potts model on Cayley tree of order three by giving all possible forms of boundary functions. We showed that the boundary functions can be described in terms of roots of some general cubic equations over some domains of p-adic field. | Degree Level: | Master | Call Number: | t QA 215 M697C 2016 | Kullliyah: | Kulliyyah of Science | Programme: | Master of Science (Computational and Theoretical Sciences) | URI: | http://studentrepo.iium.edu.my/jspui/handle/123456789/6069 | URL: | https://lib.iium.edu.my/mom/services/mom/document/getFile/klXFhaT9IseUqz8VGA1fxal5MxYl4uUa20161017121303294 |
Appears in Collections: | KOS Thesis |
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t11100345413MohdAliKhameini_SEC_24.pdf | 24 pages file | 457.15 kB | Adobe PDF | View/Open |
t11100345413MohdAliKhameini_SEC.pdf Restricted Access | Full text secured file | 3.73 MB | Adobe PDF | View/Open Request a copy |
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